What is the value of tan(pi/(24))-cot(pi/(24)) ?

The value of tan(pi/(24))-cot(pi/(24)) is -2(2+sqrt(3))

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tan(pi/(24))-cot(pi/(24))

tan (\frac{π}{24}) - cot (\frac{π}{24})

- 2 (2 + 3)

Solution steps

tan (\frac{π}{24}) - cot (\frac{π}{24})

Rewrite using trig identities:

cot (\frac{π}{24}) = \frac{1}{tan ( \frac{π}{24} )}

= tan (\frac{π}{24}) - \frac{1}{tan ( \frac{π}{24} )}

tan (\frac{π}{24}) - \frac{1}{tan ( \frac{π}{24} )} = \frac{tan ^{2} ( \frac{π}{24} ) - 1}{tan ( \frac{π}{24} )}

= \frac{tan ^{2} ( \frac{π}{24} ) - 1}{tan ( \frac{π}{24} )}

Rewrite using trig identities:

tan (\frac{π}{24}) = \frac{4 - 6 - 2}{4 + 6 + 2}

= \frac{( \frac{4 - 6 - 2}{4 + 6 + 2} ) ^{2} - 1}{\frac{4 - 6 - 2}{4 + 6 + 2}}

Simplify

\frac{( \frac{4 - 6 - 2}{4 + 6 + 2} ) ^{2} - 1}{\frac{4 - 6 - 2}{4 + 6 + 2}} : - 2 (2 + 3)

= - 2 (2 + 3)

arctan (\frac{0}{- 10})

2 - 2 cos (\frac{4 π}{3})

arcsin (1. 5^{2} - 1^{2})

\frac{cos ^{5} ( 0 )}{5}

cos (0) - cos (\frac{π}{2})

What is the value of tan(pi/(24))-cot(pi/(24)) ?
The value of tan(pi/(24))-cot(pi/(24)) is -2(2+sqrt(3))